MULTI-DIMENSIONAL RIEMANN PROBLEM OF SCALAR CONSERVATION LAW |
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| Authors: | Yang Xiaozhou |
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| Affiliation: | 1. Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom;2. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland;3. Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom;1. Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany;2. Faculty of Maritime Sciences, Kobe University, Kobe 658-0022, Japan;1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2. South China Research Center for Applied Mathematics and Interdisciplinary Studies, South China Normal University, Guangzhou, Guangdong, China;3. DICATAM, Sezione di Matematica, Università di Brescia, Via Valotti 9, 25133 Brescia, Italy;1. Department of Mathematics, University of Pennsylvania, 209 South 33rd St., Philadelphia, PA 19104, United States;2. Department of Mathematical Sciences, Seoul National University, Republic of Korea;1. College of Applied Sciences, Beijing University of Technology, Ping Le Yuan 100, Chaoyang District, Beijing 100124, PR China;2. Institute of Applied Physics and Computational Mathematics, P.O.Box 8009-28, Beijing 100088, PR China;1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária, Ilha do Fundão, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ, Brazil;2. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel;3. Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843-3368, USA;4. Department of Mathematics, Yichun University, Yichun, Jiangxi, 336000, PR China |
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| Abstract: | This paper considers multi-dimensional Riemann problem in another kind of view. The author gets solution of (1.1)(1.2) in Theorem 3.4 and proves its uniqueness. A new method of solution constructing is applied, which is different from the usual self-similar transformation. The author also discusses some generalized concepts in multi-dimensional situation (such as "convex condition", "left value" and "right value", etc). An example is finally given to demonstrate that rarefaction wave solution of (1 .1)(1 .2) is not self-similar. |
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| Keywords: | Riemann problem conservation laws implicit function. |
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